On a classification of the quasi Yamabe gradient solitons

Details On a classification of the quasi Yamabe gradient solitons On a classification of the quasi Yamabe gradient solitons

2011-08-31

arxiv.org/abs/1108.6177v1

Mathematics

Differential Geometry

11 pages

Scientific paper

In this paper, we introduce the concept of quasi Yamabe gradient solitons, which generalizes the concept of Yamabe gradient solitons. By using some ideas in [7,8], we prove that $n$-dimensional $(n\geq3)$ complete quasi Yamabe gradient solitons with vanishing Weyl curvature tensor and positive sectional curvature must be rotationally symmetric. We also prove that any compact quasi Yamabe gradient solitons are of constant scalar curvature.

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